2008/09/23 by Ugo Bruzzo, Bruzzo, Ugo, Beatriz Grana Otero +1 · 1 citation
Mathematics · #14F05 #14H60 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14F05 #msc:14H60 #msc:14J60
paper · pdf · doi:10.48550/arxiv.0809.3936
14 pages. v2: typos corrected, minor additions
arxiv created 2008/10/20 · arxiv updated 2009/12/01
We give a Miyaoka-type semistability criterion for principal Higgs G-bundles E on complex projective manifolds of any dimension, i.e., we prove that E is semistable and the second Chern class of its adjoint bundle vanishes if and only if certain line bundles, obtained from the characters of the parabolic subgroups of G, are numerically effective. We also give alternative characterizations in terms of a notion of numerical effectiveness of Higgs vector bundles we have recently introduced.